Did a significant number of women drive in late 1950s/1960s USA?

American women in the 1950s and 1960s mostly DID drive cars, so the shows are authentic. The obvious reason was that the American standard of living in those days was about 50% higher than that of the UK. A more important reason, perhaps, was subtle differences in the social roles of American, versus say, British women.

American men were the "CEO's" of their families, in those days, but women were "Vice-Presidents," and treated as such. They seldom had final decision making authority, but they were accorded "backup" roles, including the right to act for their husbands when they were absent or incapacitated. That included the right to drive cars (as in the case of MA Golding's family). The anecdote in Lars' answer about girl scouts getting the "automotive" badge bears this out.

American families of the time were what I call "one and a half" car families. That is to say, there was a larger "family" car, usually driven by the husband, and a smaller car for the wife. This would allow her to drive around to get groceries, and to take children to and from school, one or two at a time. Besides being driven to the office, the "family" car would be used for taking the whole family on weekend excursions or long vacations, usually with the husband doing most of the driving.

The smaller "wife's" car was often a "hand me down." Let's say that a couple bought a family car in 1957, the year I was born. Earlier, they would have owned a smaller car purchased in 1953 or 1954, which was the "family" car in those years, and became the "wife's" car in 1957. Around 1960-1961, the cycle would be repeated, with that year's model being the family car, and the 1957 model becoming the wife's car.

Society was very different between the USA and the UK at that time, and might account for why your observations are so different from what you saw on American TV.

My parents for instance emigrated from the UK in 1957. They were about 30 years old, but neither of them had ever driven a car.

Public transit was excellent in the UK so there was no real need for them to have learned to drive. Richer people would have had personal cars, for status or because they had houses in more out of the way places. And some people (almost all males) would have needed vehicles for their jobs (e.g. salesmen). But there was almost no need for any female to drive a car (QE-II being an obvious exception).

In Canada and the USA, except in the largest cities, an automobile was effectively a requirement of life. Post WW-II suburban communities (e.g. Levittown) were designed with the assumption that everyone had their own car. Even in many cities where there used to be useful public transit, Big Auto had managed to have these systems shut down.

My father soon learned to drive here. My mother never did get her licence.

Most young women drove, by young I mean under 50. Many did not have cars because of cost so may not have routinely driven. In those days reliability of most cars was crap and if you did not do your own work, it was very expensive. Although low income/ in college, I normally had two cars from about 58'. Then when one did not run , I used the other until I repaired it. Every year a car needed tires, brakes, plugs , points and maybe a water pump, fuel pump, voltage regulator, starter solenoid, shocks , tie rod ends, etc, etc. Not something young women were generally interested in. But it gave opportunities ; I gave a few girls driving lessons. I has a stand trans ,mild hot rod. "Give it more gas, first gear and let the clutch out , it will go, steer it ", basic lesson. Of course British cars had electronics made by Lucas, the "Prince of Darkness", so that may have been more difficult. Forgot , most older cars did not have power steering or brakes. Urban parallel parking with manual steering could be a workout , another reason why women did not routinely drive.

As I remember, my family had one car at a time during the 1950s and 1960s. My mother drove the car, as my father never learned how to drive.

I don't remember when my bothers and sisters learned to drive but all except me learned to drive before 1980, and my sisters were married and one of my brothers living eleswhere, by then.

One of my grandmothers drove and had her own car, separate from her husband's, by the 1970s, and contnued to drive in the 1980s. My other grandmother didn't have a car of her own except for relatively short periods, but I remember her driving in the 1960s and the 1970s.

Of course, I don't know how similar to an average, typical, normal, US family we were in the 1950s and 60s.

Going back even earlier, looking through advertis*m*nts in, say, National Geographic, indicates that quite a few women drove themselves even in the 1920's onward. They seemed to be the target of advertis*m*nts of automatic transmissions.

My mother (born 1936) certainly drove in the 50's and 60's. Until the mid-70's my parents had only one car, and she was the primary driver (my father could take the train to his work while she had to drive).

My mother-in-law drove across the country in 1967 with her three children in a station wagon pulling an Airstream trailer, taking them to meet with my father-in-law who did a summer sabbatical.

My grandmother and grandfather only owned one car, but both could and did drive it as needed.

Yes, more teenaged boys than girls (in my experience) owned and worked on cars (mainly because they bought cheap cars that needed work). But everyone learned to drive.

Yes, at least in non-urban areas. Certainly among high school aged women (because I'm going from personal experience). Basically everyone drove as soon as they legally could (sometimes sooner :-)). Those with enough money would have their own cars, otherwise they'd use the family car.

One thing that might give something of a wrong impression is that when there was a couple in a car, it was almost always the male driving. (That's still often the case today.) Even if the woman had her own car, for social occasions (e.g. dates) it was more acceptable for the man to use his.

The description reads as authentic.

Of course, we need to differentiate quite a bit.

The more rural it gets the earlier female adoption of driving automobiles is observed.

It seems that by 1940 most young and middle–aged farm women who were interested in mobility could and did drive the family car.

— Margaret Walsh: "Gender and the Automobile in the United States, Gender and Automobility: The Pioneering and Early Years", University of Michigan: Automobile in American Life and Society, 2004.

Then with the boom in suburbanization after the war, and the parallel destruction of most of public transport in many areas, for those living in suburbian hell, it also became a necessity.

Life in the suburbs—and by 1965 55% of those with incomes over $10,000 were suburbanites—was isolated and miserable without access to facilities. Commuting became a way of life for millions. Although these Americans were differentiated into particular communities by economic and racial discrimination, they all needed to move back and forth for work, school, shopping, running errands, and travelling to group events, whether these were religious, child-oriented, or recreational. Public transit, whether older modes like trains and streetcars or the newer bus, could not meet new individualistic aspirations and demands. The private car was the obvious practical answer, and soon there was an automobile parked on every suburban drive. Indeed, by 1960 15% of families registered ownership of two or more cars, a figure that had risen to 28% a decade later.

— Margaret Walsh: "Gender and the Automobile in the United States. Gender and Automobility: Consumerism and the Great Economic Boom", 2004. (Quotes here kept very short, go & visit.)

Of course, the very wealthy, and very poor did not drive, the former were driven, the latter driven out of participation. And in cities with good enough infrastructure kept, like New York, self-driving is somewhat optional.

Without watching Perry Mason just to check this, typical TV series depict mostly quite well-off upper middle class people. Those were at the timeframe given freshly sent to and bred in various suburbias. So they at the same time had to drive themselves, and of course another necessity: if they wouldn't have done that, we would have never seen one of those female drivers on screen as hey would have been hidden in hideous small homes, far away from any action a camera or screenwriter is usually interested in…